What is the derivative of (x^3+1^{1/2}) ?

The derivative of (x^3+1^{1/2}) is (3x^2)/(2(x^3+1)^{1/2)}

What is the first derivative of (x^3+1^{1/2}) ?

The first derivative of (x^3+1^{1/2}) is (3x^2)/(2(x^3+1)^{1/2)}

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\frac{d}{d x} ((x^{3} + 1)^{\frac{1}{2}})

\frac{3 x ^{2}}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((x^{3} + 1)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}} \frac{d}{d x} (x^{3} + 1)

= \frac{1}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}} \frac{d}{d x} (x^{3} + 1)

\frac{d}{d x} (x^{3} + 1) = 3 x^{2}

= \frac{1}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}} \cdot 3 x^{2}

Simplify

\frac{1}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}} \cdot 3 x^{2} : \frac{3 x ^{2}}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}}

= \frac{3 x ^{2}}{2 ( x ^{3} + 1 ) ^{\frac{1}{2}}}

What is the derivative of (x^3+1^{1/2}) ?
The derivative of (x^3+1^{1/2}) is (3x^2)/(2(x^3+1)^{1/2)}
What is the first derivative of (x^3+1^{1/2}) ?
The first derivative of (x^3+1^{1/2}) is (3x^2)/(2(x^3+1)^{1/2)}